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Weighted $$1\times 1$$ 1 × 1 Cut-and-Project Sets in Bounded Distance to a Lattice

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 04 May 2018Embargo end date: 01 Jan 2017 Germany Publisher:Springer Science and Business Media LLCJournal:Discrete & Computational Geometry, volume 62, pages 649-661 (issn: 0179-5376, eissn: 1432-0444,

Authors: Frettlöh, Dirk; Garber, Alexey;

doi: 10.1007/s00454-018-0005-1 , 10.48550/arxiv.1706.01089

arXiv: http://arxiv.org/abs/1706.01089

Weighted $$1\times 1$$ 1 × 1 Cut-and-Project Sets in Bounded Distance to a Lattice

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Abstract

Recent results of Grepstad and Lev are used to show that weighted cut-and-project sets with one-dimensional physical space and one-dimensional internal space are bounded distance equivalent to some lattice if the weight function $h$ is continuous on the internal space, and if $h$ is either piecewise linear, or twice differentiable with bounded curvature.

11 pages, 1 figure

Country

Germany

Related Organizations

Bielefeld University
Germany
University of the West
United States
The University of Texas Rio Grande Valley
United States

Keywords

Mathematics - Metric Geometry, Bounded remainder, FOS: Mathematics, Metric Geometry (math.MG), Bounded distance equivalence, sets, Cut-and-project sets, 52C23, 37E54, 11J83

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